Surfaces of revolution Suppose y = f ( x ) is a continuous and positive function on [ a, b ] . Let S be the surface generated when the graph of f on [ a, b ] is revolved about the x -axis. a. Show that S is described parametrically by r ( u , v ) = 〈 u, f ( u ) cos v, f ( u ) sin v 〉, for a ≤ u ≤ b , 0 ≤ v ≤ 2 π. b. Find an integral that gives the surface area of S . c. Apply the result of part (b) to find the area of the surface generated with f ( x ) = x 3 , for 1 ≤ x ≤ 2 . d. Apply the result of part (b) to find the area of the surface generated with f ( x ) = (25 – x 2 ) 1/2 , for 3 ≤ x ≤ 4.
Surfaces of revolution Suppose y = f ( x ) is a continuous and positive function on [ a, b ] . Let S be the surface generated when the graph of f on [ a, b ] is revolved about the x -axis. a. Show that S is described parametrically by r ( u , v ) = 〈 u, f ( u ) cos v, f ( u ) sin v 〉, for a ≤ u ≤ b , 0 ≤ v ≤ 2 π. b. Find an integral that gives the surface area of S . c. Apply the result of part (b) to find the area of the surface generated with f ( x ) = x 3 , for 1 ≤ x ≤ 2 . d. Apply the result of part (b) to find the area of the surface generated with f ( x ) = (25 – x 2 ) 1/2 , for 3 ≤ x ≤ 4.
Solution Summary: The author explains that the surface S is generated when the graph of f on left[a,bright] is revolved about the x -axis, the center of the circle will be on
Surfaces of revolution Suppose y = f(x) is a continuous and positive function on [a, b]. Let S be the surface generated when the graph of f on [a, b] is revolved about the x-axis.
a. Show that S is described parametrically by r(u, v) = 〈u, f(u) cos v, f(u) sin v〉, for a ≤ u ≤ b, 0 ≤ v ≤ 2 π.
b. Find an integral that gives the surface area of S.
c. Apply the result of part (b) to find the area of the surface generated with f(x) = x3, for 1 ≤ x ≤ 2.
d. Apply the result of part (b) to find the area of the surface generated with f(x) = (25 – x2)1/2, for 3 ≤ x ≤ 4.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.